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Mirrors > Home > ILE Home > Th. List > tsetslid | GIF version |
Description: Slot property of TopSet. (Contributed by Jim Kingdon, 9-Feb-2023.) |
Ref | Expression |
---|---|
tsetslid | ⊢ (TopSet = Slot (TopSet‘ndx) ∧ (TopSet‘ndx) ∈ ℕ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tset 12605 | . 2 ⊢ TopSet = Slot 9 | |
2 | 9nn 9116 | . 2 ⊢ 9 ∈ ℕ | |
3 | 1, 2 | ndxslid 12536 | 1 ⊢ (TopSet = Slot (TopSet‘ndx) ∧ (TopSet‘ndx) ∈ ℕ) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 = wceq 1364 ∈ wcel 2160 ‘cfv 5235 ℕcn 8948 9c9 9006 ndxcnx 12508 Slot cslot 12510 TopSetcts 12592 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-cnex 7931 ax-resscn 7932 ax-1re 7934 ax-addrcl 7937 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-iota 5196 df-fun 5237 df-fv 5243 df-ov 5898 df-inn 8949 df-2 9007 df-3 9008 df-4 9009 df-5 9010 df-6 9011 df-7 9012 df-8 9013 df-9 9014 df-ndx 12514 df-slot 12515 df-tset 12605 |
This theorem is referenced by: topgrptsetd 12707 topnfn 12746 topnvalg 12753 mgptsetg 13279 sratsetg 13758 topontopn 13989 setsmsdsg 14432 setsmstsetg 14433 |
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